On the stability of surfaces of stressed solids

Abstract

A simple linear stability analysis is presented which demonstrates that the nominally flat surface of an elastically stressed body is unstable with respect to the growth of perturbations with wavelengths greater than a critical wavelength. For a solid, constrained in one dimension and subject to a uniform dilatation, this wavelength scales as [gamma]E/[sigma]2, where [gamma] is the surface energy, E is Young's modulus, and [sigma] is the nominal stress associated with the constrained dilatation. The maximally unstable mode depends on the manner of matter transport (surface diffusion and evaporation/condensation are considered). The predicted wavelength of the instability is consistent with observations of thin InGaAs films grown on GaAs.